Page 399 - Marine Structural Design

Chapter 20 Spectral Fatigue Analysis and Design 315

where n(S)dS represents the number of stress ranges between S and S+dS. If a stationary
response process of duration TIir, is assumed, the total number of stress cycles will be:
n(S)dS = vOiir;i/p(S)dS (20.4)

where the zero-up crossing frequency Voi is
-

(20.5)

where,
moi = Spectral zero moment of the hotspot stress spectrum
m,,, = Spectral second moment of the hotspot stress spectrum
The Rayleigh probability density function for stress range S is:

(20.6)

where the root mean square stress ci is

(Ti =& (20.7)
Then, one can obtain:

(20.8)

Using the following notation,
S2
x=- (20.9)
SOi*

and Gamma function:

(20.10)

We may get:

(20.1 1)

Fatigue Damage for All Sea-States
From the damage equation for one sea-state, one may easily calculate the damage accumulated
for all sea-states.